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April 2021 Nonlinear *-Jordan-type derivations on *-algebras
Changjing Li, Yuanyuan Zhao, Fangfang Zhao
Rocky Mountain J. Math. 51(2): 601-612 (April 2021). DOI: 10.1216/rmj.2021.51.601

Abstract

Let 𝒜 be a unital -algebra with the unit I. Assume that 𝒜 contains a nontrivial projection P which satisfies X𝒜P=0 implies X=0 and X𝒜(IP)=0 implies X=0. In this paper, it is shown that Φ is a nonlinear -Jordan-type derivation on 𝒜 if and only if Φ is an additive -derivation. As applications, the nonlinear -Jordan-type derivations on prime -algebras, von Neumann algebras with no central summands of type I1, factor von Neumann algebras and standard operator algebras are characterized.

Citation

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Changjing Li. Yuanyuan Zhao. Fangfang Zhao. "Nonlinear *-Jordan-type derivations on *-algebras." Rocky Mountain J. Math. 51 (2) 601 - 612, April 2021. https://doi.org/10.1216/rmj.2021.51.601

Information

Received: 22 June 2020; Revised: 21 September 2020; Accepted: 16 October 2020; Published: April 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.1216/rmj.2021.51.601

Subjects:
Primary: 47B47
Secondary: 46L10

Keywords: *-derivations , *-Jordan-type derivations , von Neumann algebras

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 2 • April 2021
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